The Traditional Mass is not a separate rite.
It could be.
RITES
A Rite represents an ecclesiastical, or church, tradition about how the sacraments are to be celebrated. Each of the sacraments has at its core an essential nature which must be satisfied for the sacrament to be confected or realized. This essence - of matter, form and intention - derives from the divinely revealed nature of the particular sacrament. It cannot be changed by the Church. Scripture and Sacred Tradition, as interpreted by the Magisterium, tells us what is essential in each of the sacraments (2 Thes. 2:15).
When the apostles brought the Gospel to the major cultural centers of their day the essential elements of religious practice were inculturated into those cultures. This means that the essential elements were clothed in the symbols and trappings of the particular people, so that the rituals conveyed the desired spiritual meaning to that culture. In this way the Church becomes all things to all men that some might be saved (1 Cor. 9:22).
There are three major groupings of Rites based on this initial transmission of the faith, the Roman, the Antiochian (Syria) and the Alexandrian (Egypt). Later on the Byzantine derived as a major Rite from the Antiochian, under the influence of St. Basil and St. John Chrysostom. From these four derive the over 20 liturgical Rites present in the Church today.
Western Rites and Churches
Immediately subject to the Supreme Pontiff as Patriarch of the West
ROMAN (also called Latin)
The Church of Rome is the Primatial See of the world and the Patriarchal See of Western Christianity. Founded by St. Peter in 42 AD it was consecrated by the blood of Sts. Peter and Paul during the persecution of Nero (63-67 AD). It has maintained a continual existence since then and is the source of a family of Rites in the West. Considerable scholarship (such as that of Fr. Louis Boyer in Eucharist) suggests the close affinity of the Roman Rite proper with the Jewish prayers of the synagogue, which also accompanied the Temple sacrifices. While the origin of the current Rite, even in the reform of Vatican II, can be traced directly only to the 4th century, these connections point to an ancient apostolic tradition brought to that city that was decidedly Jewish in origin.
Roman - The overwhelming majority of Latin Catholics and of Catholics in general. Patriarch of this and the other Roman Rites is the Bishop of Rome. The current Roman Rite is that of the 1969 Missale Romanum, to be published in a third edition in 2001.
- Missal of 1962 (Tridentine Mass) - Some institutes within the Roman Rite, such as the Priestly Fraternity of St. Peter, have the faculty to celebrate the sacramental rites according to the forms in use prior to the Second Vatican Council. This faculty can also be obtained by individual priests from their bishop or from the Pontifical Council Ecclesia Dei.
- Anglican Use - Since the 1980s the Holy See has granted some former Anglican and Episcopal clergy converting with their parishes the faculty of celebrating the sacramental rites according to Anglican forms, doctrinally corrected.
Mozarabic - The Rite of the Iberian peninsula (Spain and Portugal) known from at least the 6th century, but probably with roots to the original evangelization. Beginning in the 11th century it was generally replaced by the Roman Rite, although it has remained the Rite of the Cathedral of the Archdiocese of Toledo, Spain, and six parishes which sought permission to adhere to it. Its celebration today is generally semi-private.
Ambrosian - The Rite of the Archdiocese of Milan, Italy, thought to be of early origin and probably consolidated, but not originated, by St. Ambrose. Pope Paul VI was from this Roman Rite. It continues to be celebrated in Milan, though not by all parishes.
Bragan - Rite of the Archdiocese of Braga, the Primatial See of Portugal, it derives from the 12th century or earlier. It continues to be of occasional use.
Dominican - Rite of the Order of Friars Preacher (OP), founded by St. Dominic in 1215.
Carmelite - Rite of the Order of Carmel, whose modern foundation was by St. Berthold c.1154.
Carthusian - Rite of the Carthusian Order founded by St. Bruno in 1084.